The Lennard-Jones potential

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Potential form

  • The Lennard-Jones (LJ) potential is one the most simplest two-body potentials used in MD simulations. The pair potential between particles [math]i[/math] and [math]j[/math] is

$$ U_{ij} = 4 \epsilon_{ij} \left( \frac{ \sigma_{ij}^{12} }{ r_{ij}^{12} } - \frac{\sigma_{ij}^{6} }{ r_{ij}^{6} } \right). $$

Parameters

Parameter Units
[math]\epsilon_{ij}[/math] eV
[math]\sigma_{ij}[/math] A

Potential file format

  • If there is only one atom type, the potential file for this potential model reads
   lj 1
   epsilon sigma cutoff

Here, cutoff is the cutoff distance.

  • If there are two atom types, the potential file reads
   lj 2
   epsilon_00 sigma_00 cutoff_00
   epsilon_01 sigma_01 cutoff_01
   epsilon_10 sigma_10 cutoff_10
   epsilon_11 sigma_11 cutoff_11
  • If there are three atom types, the potential file reads
   lj 3
   epsilon_00 sigma_00 cutoff_00
   epsilon_01 sigma_01 cutoff_01
   epsilon_02 sigma_02 cutoff_02
   epsilon_10 sigma_10 cutoff_10
   epsilon_11 sigma_11 cutoff_11
   epsilon_12 sigma_12 cutoff_12
   epsilon_20 sigma_20 cutoff_20
   epsilon_21 sigma_21 cutoff_21
   epsilon_22 sigma_22 cutoff_22
  • I hope the reader can understand the pattern and figure out how to prepare potential files with four and five atom types.

Tips

  • The current version of GPUMD supports up to five atom types for the LJ potential.
  • The potential has not been shifted.